{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# numpy is a python pkg\n",
    "# what import does? just run that file\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use(\"ggplot\") # just for style preferrence\n",
    "import matplotlib_inline as mpli\n",
    "mpli.backend_inline.set_matplotlib_formats(\"svg\") # svg is clearer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to make Abstraction?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Give name: Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.1, 'hello world from Python!')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 2.1\n",
    "y = \"hello world from Python!\"\n",
    "x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "315"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 15\n",
    "y = 21\n",
    "x*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Hello Zhejiang University'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = \"Zhejiang\"\n",
    "y = \"University\"\n",
    "'Hello'+' '+x+\" \"+y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Happy   125   Birthday to Zhejiang University'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 格式化字符串 format string\n",
    "x = \"Zhejiang\"\n",
    "y = \"University\"\n",
    "years = 125\n",
    "f\"Happy {years:^7} Birthday to {x} {y}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1;31mInit signature:\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m/\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mDocstring:\u001b[0m     \n",
      "range(stop) -> range object\n",
      "range(start, stop[, step]) -> range object\n",
      "\n",
      "Return an object that produces a sequence of integers from start (inclusive)\n",
      "to stop (exclusive) by step.  range(i, j) produces i, i+1, i+2, ..., j-1.\n",
      "start defaults to 0, and stop is omitted!  range(4) produces 0, 1, 2, 3.\n",
      "These are exactly the valid indices for a list of 4 elements.\n",
      "When step is given, it specifies the increment (or decrement).\n",
      "\u001b[1;31mType:\u001b[0m           type\n",
      "\u001b[1;31mSubclasses:\u001b[0m     \n"
     ]
    }
   ],
   "source": [
    "range?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0th iteration: this that,...\n",
      "1th iteration: this that,...\n",
      "2th iteration: this that,...\n",
      "3th iteration: this that,...\n",
      "4th iteration: this that,...\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    print(f\"{i}th iteration: this that,...\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5050"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 循环\n",
    "s=0\n",
    "for i in range(101):\n",
    "    s+=i\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2550"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 条件\n",
    "s=0\n",
    "for i in range(101):\n",
    "    if i%2 == 0:\n",
    "        s+=i\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1adf1ea3bb0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,1,10)\n",
    "plt.scatter(x,f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f():\n",
    "    \"\"\"return tuple\"\"\"\n",
    "    return 10,\"hi\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 'hi')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a,b = f()\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'hi'"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,y):\n",
    "    return 10*x + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 元组拆包\n",
    "t = (1,18)\n",
    "f(*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "# default parameters\n",
    "def f(id,depart=3):\n",
    "    if depart ==3 :\n",
    "        return f\"3 + {id}\"\n",
    "    else:\n",
    "        return \"Not in Depart. 3!\"\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3 + 318'"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(\"318\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Not in Depart. 3!'"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(\"318\",1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Object and Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 3, 2, 1, 1, 0]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = list(range(5))\n",
    "x.append(1)\n",
    "x.sort()\n",
    "x.reverse()\n",
    "x\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Container"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Iterable\n",
    "Std Python data container:\n",
    "* list\n",
    "* dict\n",
    "* set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4]"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# list\n",
    "x = [1,2,3,4]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# index\n",
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hjc': 12, 'dlm': 6}"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dict : key-value map\n",
    "name_birth = {\n",
    "    \"hjc\":12,\n",
    "    \"dlm\":6\n",
    "}\n",
    "name_birth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name_birth[\"hjc\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "name_birth[\"wzh\"] = 13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hjc': 12, 'dlm': 6, 'wzh': 13}"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name_birth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elementwise Operation and Fancy Indexing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explore NumPy ndarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(10.)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.25, 0.5 , 0.75, 1.  ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0,1,5)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 2.],\n",
       "       [3., 4., 5.],\n",
       "       [6., 7., 8.]])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(9.).reshape(3,3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(6).reshape(2,3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 3],\n",
       "       [1, 4],\n",
       "       [2, 5]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8.])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fancy indexing\n",
    "x = np.arange(9.)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6.])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0:7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 2.],\n",
       "       [3., 4., 5.],\n",
       "       [6., 7., 8.]])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(9.).reshape(3,-1)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1.])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0, 0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1.],\n",
       "       [3., 4.]])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0:2,0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False],\n",
       "       [False, False,  True],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x>4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5., 6., 7., 8.])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[x>4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0., 1., 2.]), array([5., 6., 9.]))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# element wise operation\n",
    "x = np.arange(3.)\n",
    "y = np.array([5.,6.,9.])\n",
    "x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 5.,  7., 11.]), array([-5., -5., -7.]))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + y, x-y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  6., 18.])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  6., 81.])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y**x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 2., 4.])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 0.,  1.,  2.],\n",
       "        [ 3.,  4.,  5.],\n",
       "        [ 6.,  7.,  8.],\n",
       "        [ 9., 10., 11.]]),\n",
       " array([0., 1., 2.]))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(12.).reshape(4,3)\n",
    "y = np.arange(3.)\n",
    "x,y\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  4.],\n",
       "       [ 0.,  4., 10.],\n",
       "       [ 0.,  7., 16.],\n",
       "       [ 0., 10., 22.]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5., 14., 23., 32.])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(x*y,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x257774c3fa0>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# matlab-style interface\n",
    "# simple\n",
    "x = np.linspace(-1,1,10)\n",
    "plt.scatter(x,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 4)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(12.).reshape(3,-1)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10,)"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(10.)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.74804884,  0.48424629, -0.03073617,  0.83685934])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-2,2,20)\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(x,0.5*x + np.cos(x),\"--\",\n",
    "        c='blue',\n",
    "        label=\"Analytical\")\n",
    "ax.scatter(x,0.5*x+np.cos(x) + np.random.randn(*x.shape), \n",
    "            alpha=.6,\n",
    "            label=\"Measure\")\n",
    "ax.set_xlabel(\"Volt(V)\")\n",
    "ax.set_ylabel(\"Current(A)\")\n",
    "t_title=\"VI Plot\"\n",
    "ax.set_title(t_title)\n",
    "ax.legend()\n",
    "\n",
    "fig.suptitle(\"Suptitle\")\n",
    "fig.savefig(f\"{t_title}.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# oop style\n",
    "# fine-grained\n",
    "x = np.linspace(-1,1,10)\n",
    "fig,ax = plt.subplots(2,3)\n",
    "# ax.plot(x,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:>, <AxesSubplot:>, <AxesSubplot:>],\n",
       "       [<AxesSubplot:>, <AxesSubplot:>, <AxesSubplot:>]], dtype=object)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2577750a0d0>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax[0,0].scatter(x,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
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     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 5., 6., 9.])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "np.concatenate((x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Broadcasting\n",
    "<img src=\"./pics/broadcasting.png\">  \n",
    "\n",
    "(cite from Python Datascience Handbook)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples: Calcultating mean of random variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Geometric Distribution(几何分布) $X\\sim G(p)$:  \n",
    "$$\n",
    "P(X = k) = {(1-p)}^{k-1} p, k = 1,2,\\dots\n",
    "$$\n",
    "The analytical result is $E[X] = \\frac1p$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.978515625"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fast, script style\n",
    "NUM = 10 # act as a cut_off\n",
    "p = 0.5\n",
    "x = np.arange(1,NUM)\n",
    "np.sum( (p*(1-p)**(x-1)) * x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(3.)\n",
    "y = x.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 2., 4.]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "y**x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# more reusable style, and try to varify the analytical result\n",
    "class Geometric():\n",
    "    def __init__(self,p):\n",
    "        self.p = p\n",
    "    def __call__(self,x):\n",
    "        \"\"\" callable interface \"\"\"\n",
    "        p = self.p.reshape(-1,1)\n",
    "        return p* (1-p) **(x-1)\n",
    "    def mean(self):\n",
    "        NUM = 100\n",
    "        x = np.arange(1,NUM)\n",
    "        return np.sum(self(x) * x,axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 1)\n"
     ]
    },
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     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1adf5cf7430>"
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eps = 1e-1\n",
    "p = np.linspace(eps,1,10)\n",
    "analytic = 1/p\n",
    "numeric = Geometric(p).mean()\n",
    "fig,ax = plt.subplots()\n",
    "ax.plot(p,analytic,label=\"analytic\")\n",
    "ax.scatter(p,numeric,label=\"numeric\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exponential Distribution $X\\sim E($:  \n",
    "$$\n",
    "P(X)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Organizing Tabular Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explore Pandas Series and DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
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